Finite Group Databasebeta

← #11909800

Subgroups — #11909800

Order 1152.

2314 conjugacy classes of subgroups.

The subgroup lattice has 946 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596193C211yesmaximal, characteristic, complemented
2C3×#5730C211yesmaximal, characteristic, complemented
3C3×#5725C211yesmaximal, characteristic, complemented
4#10595391C214yesmaximal, complemented
5#10595357C214yesmaximal, complemented
6#10594592C212yesmaximal, complemented
7#10594582C212yesmaximal, complemented
8#10594525C212yesmaximal, complemented
9#10594485C212yesmaximal, complemented
10#10594427C212yesmaximal, complemented
11#10594370C212yesmaximal, complemented
12#10594367C212yesmaximal, complemented
13#10594359C212yesmaximal, complemented
14#10593974C211yesmaximal, characteristic, complemented
15#10593951C211yesmaximal, characteristic, complemented
16#10593906C211yesmaximal, characteristic, complemented
17C4×D3×Dic6C211yesmaximal, characteristic, complemented
18#86936—31nomaximal
19#86229—31nomaximal
20C2×C3×#239C2212yes—
21C2×#3795C2212yes—
22C2×#3795C2214yes—
23C2×D3×Dic6C2211yescharacteristic
24C32×C4⋊Q8C2211yescharacteristic
25#64153C2214yes—
26#64097C2212yes—
27#64097C2212yes—
28#64096C2212yes—
29#64096C2212yes—
30C4×#634C2211yescharacteristic
31C4×#634C2211yescharacteristic
32C3×#947C2212yes—
33C3×#946C2214yes—
34C3×#897C2212yes—
35C3×#895C2212yes—
36C3×#895C2212yes—
37C3×#893C2212yes—
38C3×#893C2212yes—
39C3×#893C2212yes—
40C3×D3×C4⋊C4C2212yes—
41C3×#890C2212yes—
42C3×#874C2211yescharacteristic
43C3×C4×D12C2211yescharacteristic
44C3×C42×D3C2211yescharacteristic
45C3×C4×Dic6C2211yescharacteristic
46C4×#627C2212yes—
47#63915C2214yes—
48#63914C2212yes—
49#63913C2214yes—
50#63908C2212yes—
51#63908C2211yescharacteristic
52#63905C2214yes—
53#63905C2214yes—
54#63905C2212yes—
55C4×#625C2214yes—
56C4×#625C2212yes—
57#63899C2214yes—
58#63898C2214yes—
59#63898C2212yes—
60#63898C2212yes—
61#63896C2214yes—
62Dic3×D12C2212yes—
63D3×C4⋊Dic3C2211yescharacteristic
64#63885C2214yes—
65#63885C2214yes—
66#63884C2214yes—
67#63884C2214yes—
68#63879C2214yes—
69#63878C2214yes—
70D3×Dic3⋊C4C2212yes—
71D3×Dic3⋊C4C2214yes—
72C4×D3×Dic3C2212yes—
73#63869C2211yescharacteristic
74#63863C2212yes—
75#63860C2211yescharacteristic
76#63860C2212yes—
77#63859C2212yes—
78#63858C2214yes—
79#63857C2214yes—
80#63857C2211yescharacteristic
81#63855C2212yes—
82#63844C2211yescharacteristic
83Dic3×Dic6C2211yescharacteristic
84#63837C2212yes—
85C3×#554—31no—
86C3×#532—31no—
87#5824—34no—
88#5730D311yescharacteristic, complemented
89#5725D311yescharacteristic, complemented
90#5722—31no—
91#5722—31no—
92#5722—61no—
93#5718—31no—
94#5713—31no—
95#5691—32no—
96#5690—32no—
97#5669—34no—
98#5643—32no—
99#5640—34no—
100#5633—32no—
101#5631—34no—
102#5611—32no—
103#5600—32no—
104#5598—32no—
105#5596—32no—
106#5585—31no—
107C4×D3×Q8—31no—
108#5561—32no—
109#5559—32no—
110#5559—32no—
111#5557—31no—
112#5553—31no—
113#5548—32no—
114#5546—32no—
115#5539—32no—
116#5507—32no—
117#5504—32no—
118#5479—31no—
119C2×C4×Dic6—31no—
120C2×C32×Q8C2312yes—
121C2×#634C2311yescharacteristic
122C2×#634C2314yes—
123C2×#634C2311yescharacteristic
124C3×#239—44no—
125C2×C3×D12C2311yescharacteristic
126C2×C3×D12C2312yes—
127C2×C3×D12C2312yes—
128C2×C3×D12C2314yes—
129C2×C3×D12C2312yes—
130C2×C3×C4×D3C2312yes—
131C2×C3×C4×D3C2311yescharacteristic
132C2×C3×C4×D3C2311yescharacteristic
133C2×C3×C4×D3C2311yescharacteristic
134C2×C3×C4×D3C2314yes—
135C2×C3×C4×D3C2314yes—
136C2×C3×Dic6C2311yescharacteristic
137C2×#627C2312yes—
138C2×#625C2312yes—
139C2×#625C2314yes—
140C2×#625C2314yes—
141C2×D3×Dic3C2312yes—
142C2×D3×Dic3C2312yes—
143C2×D3×Dic3C2314yes—
144C2×D3×Dic3C2314yes—
145#3795—28no—
146#3795—48no—
147D3×Dic6—24no—
148C32×C4⋊C4C2312yes—
149C32×C4⋊C4C2312yes—
150C32×C42C2311yescharacteristic
151C4⋊(C3⋊Dic3)C2311yescharacteristic
152C4⋊(C3⋊Dic3)C2311yescharacteristic
153#3750C2312yes—
154#3750C2312yes—
155#3750C2314yes—
156#3750C2314yes—
157C4×C3⋊Dic3C2312yes—
158C4×C3⋊Dic3C2312yes—
159C4×C3⋊Dic3C2314yes—
160C3×(C2×D3)⋊C4C2314yes—
161C3×(C2×D3)⋊C4C2314yes—
162C3×(C2×D3)⋊C4C2314yes—
163C3×(C2×D3)⋊C4C2312yes—
164C3×C4⋊Dic3C2311yescharacteristic
165C3×C4⋊Dic3C2314yes—
166C3×C4⋊Dic3C2311yescharacteristic
167C3×Dic3⋊C4C2314yes—
168C3×Dic3⋊C4C2312yes—
169C3×C4×Dic3C2312yes—
170C3×C4×Dic3C2311yescharacteristic
171C3×C4×Dic3C2311yescharacteristic
172C3×C4×Dic3C2311yescharacteristic
173#3724C2312yes—
174#3724C2312yes—
175Dic3⋊Dic3C2312yes—
176Dic3⋊Dic3C2312yes—
177Dic3⋊Dic3C2312yes—
178Dic3⋊Dic3C2312yes—
179(C2×D3)⋊Dic3C2312yes—
180(C2×D3)⋊Dic3C2312yes—
181(C2×D3)⋊Dic3C2314yes—
182(C2×D3)⋊Dic3C2314yes—
183(C2×D3)⋊Dic3C2312yes—
184(C2×D3)⋊Dic3C2314yes—
185(C2×D3)⋊Dic3C2312yes—
186(C2×D3)⋊Dic3C2314yes—
187Dic32C2312yes—
188Dic32C2312yes—
189#3522—91noSylow
190C2×C3×#41—32no—
191C2×#239C2×D312yes—
192C2×D3×Q8—31no—
193C2×#237—32no—
194C2×#237—34no—
195C2×#235—32no—
196C2×#235—34no—
197C22×Dic6—31no—
198C3×C4⋊Q8—21no—
199C3×C4⋊Q8C2×D311yescharacteristic
200C3×C4⋊Q8C2×D311yescharacteristic
201C3×#127—31no—
202C3×#125—32no—
203C3×#124—32no—
204C3×C22⋊Q8—34no—
205C3×C22⋊Q8—32no—
206C3×#121—32no—
207C3×#121—32no—
208C3×C4×Q8—31no—
209C3×C4×D4—32no—
210C3×C4×D4—32no—
211C3×C4×D4—32no—
212C3×C4×D4—31no—
213C2×C3×C4⋊C4—32no—
214C2×C3×C42—31no—
215#947—32no—
216#947C2×D312yes—
217#946C2×D314yes—
218Q8×Dic3—31no—
219#944—34no—
220#944—34no—
221#944—64no—
222#940—32no—
223#940—32no—
224#939—34no—
225#939—34no—
226#938—32no—
227#938—31no—
228#936—32no—
229#936—32no—
230#936—31no—
231#935—34no—
232#935—34no—
233D4×Dic3—32no—
234D4×Dic3—32no—
235D4×Dic3—34no—
236D4×Dic3—32no—
237#930—32no—
238#930—31no—
239#929—34no—
240#929—32no—
241#929—34no—
242C4×#67—32no—
243C4×#67—32no—
244C4×#67—34no—
245C4×#67—34no—
246C4×#67—34no—
247#926—32no—
248C2×C4⋊Dic3—31no—
249#924—31no—
250#924—34no—
251C2×Dic3⋊C4—32no—
252C2×Dic3⋊C4—34no—
253C2×C4×Dic3—32no—
254#898—34no—
255#897—34no—
256#897—31no—
257#897C2×D312yes—
258#896—34no—
259#896—34no—
260#895C2×D312yes—
261#895C2×D312yes—
262#894—34no—
263#894—34no—
264#893—34no—
265#893—32no—
266#893—32no—
267#893C2×D312yes—
268#893C2×D312yes—
269#893C2×D312yes—
270#892—34no—
271D3×C4⋊C4—34no—
272D3×C4⋊C4—31no—
273D3×C4⋊C4—32no—
274D3×C4⋊C4C2×D312yes—
275#890—31no—
276#890C2×D312yes—
277#888—32no—
278#888—32no—
279#888—32no—
280#888—32no—
281#888—62no—
282#888—62no—
283#887—32no—
284#887—32no—
285#887—32no—
286#887—32no—
287#887—32no—
288#887—31no—
289#887—62no—
290#887—62no—
291#885—34no—
292#885—34no—
293#885—34no—
294#885—34no—
295#884—34no—
296#884—34no—
297#883—34no—
298#883—34no—
299#883—32no—
300#67⋊C4—34no—
301#879—34no—
302#879—32no—
303#878—34no—
304#878—34no—
305#877—34no—
306#876—32no—
307#875—32no—
308#875—31no—
309#874C2×D311yescharacteristic
310C4×D12—32no—
311C4×D12C2×D311yescharacteristic
312#872—32no—
313C42×D3—32no—
314C42×D3C2×D311yescharacteristic
315#870—31no—
316C4×Dic6—31no—
317C4×Dic6—31no—
318C4×Dic6—31no—
319C4×Dic6—31no—
320C4×Dic6—31no—
321C4×Dic6—31no—
322C4×Dic6—32no—
323C4×Dic6—32no—
324C4×Dic6—32no—
325C4×Dic6—61no—
326C4×Dic6—61no—
327C4×Dic6C2×D311yescharacteristic
328C22×C3×D3C2414yes—
329C22×C3×D3C2412yes—
330C22×C3×D3C2411yescharacteristic
331C32×Q8—42no—
332C2×C32×C4C2411yescharacteristic
333C2×C32×C4C2414yes—
334C2×C32×C4C2411yescharacteristic
335C2×C32×C4C2411yescharacteristic
336C2×C3⋊Dic3C2412yes—
337C2×C3⋊Dic3C2412yes—
338C2×C3⋊Dic3C2412yes—
339C2×C3⋊Dic3C2412yes—
340#634—22no—
341#634—44no—
342#634#4114yescomplemented
343C2×C3×Dic3C2411yescharacteristic
344C2×C3×Dic3C2412yes—
345C2×C3×Dic3C2412yes—
346C2×C3×Dic3C2412yes—
347C2×C3×Dic3C2411yescharacteristic
348C2×C3×Dic3C2411yescharacteristic
349C3×D12—28no—
350C3×D12—24no—
351C3×D12—22no—
352C3×D12—24no—
353C3×D12—42no—
354C3×C4×D3—22no—
355C3×C4×D3—22no—
356C3×C4×D3—24no—
357C3×C4×D3—22no—
358C3×C4×D3—44no—
359C3×C4×D3—44no—
360C3×Dic6—22no—
361#627—24no—
362#625—24no—
363#625—28no—
364#625—44no—
365D3×Dic3—24no—
366D3×Dic3—24no—
367D3×Dic3—28no—
368D3×Dic3—44no—
369#559—92no—
370#559—91no—
371Q82—91no—
372#554—31no—
373#554—92no—
374#550—91no—
375#548—92no—
376#547—92no—
377#547—94no—
378#542—92no—
379#542—94no—
380#532—31no—
381#532—92no—
382#529—91no—
383#529—92no—
384#520—92no—
385C2×C4×Q8—91no—
386C3×#41—124no—
387C2×C3×Q8—22no—
388C2×C3×Q8—31no—
389C2×C3×Q8C22×D312yes—
390C2×C3×Q8C22×D312yes—
391C2×C3×D4—32no—
392C2×C3×D4—34no—
393C2×C3×D4—32no—
394C2×C3×D4—31no—
395C2×C3×D4—32no—
396C22×C3×C4—31no—
397C22×C3×C4—31no—
398C22×C3×C4—31no—
399C22×C3×C4—32no—
400C22×C3×C4—34no—
401C22×C3×C4—34no—
402C2×#67—34no—
403C2×#67—32no—
404C2×#67—34no—
405C2×#67—32no—
406C2×#67—34no—
407C2×#67—34no—
408C22×Dic3—34no—
409C22×Dic3—32no—
410C22×Dic3—32no—
411C22×Dic3—34no—
412#239—44no—
413D3×Q8—64no—
414#237—68no—
415#237—128no—
416#235—68no—
417#235—128no—
418C2×D12C22×D312yes—
419C2×D12C22×D311yescharacteristic
420C2×D12C22×D312yes—
421C2×D12C22×D314yes—
422C2×D12C22×D312yes—
423C2×C4×D3—32no—
424C2×C4×D3—32no—
425C2×C4×D3—34no—
426C2×C4×D3—34no—
427C2×C4×D3C22×D311yescharacteristic
428C2×C4×D3C22×D311yescharacteristic
429C2×C4×D3C22×D311yescharacteristic
430C2×C4×D3C22×D312yes—
431C2×C4×D3C22×D314yes—
432C2×C4×D3C22×D314yes—
433C2×Dic6—31no—
434C2×Dic6—31no—
435C2×Dic6—31no—
436C2×Dic6—31no—
437C2×Dic6—32no—
438C2×Dic6—32no—
439C2×Dic6—34no—
440C2×Dic6—34no—
441C2×Dic6—61no—
442C2×Dic6—61no—
443C2×Dic6—64no—
444C2×Dic6—64no—
445C2×Dic6C22×D311yescharacteristic
446C3×C4⋊C4—22no—
447C3×C4⋊C4—22no—
448C3×C4⋊C4—31no—
449C3×C4⋊C4—32no—
450C3×C4⋊C4—31no—
451C3×C4⋊C4—34no—
452C3×C4⋊C4—34no—
453C3×C4⋊C4C22×D312yes—
454C3×C4⋊C4C22×D312yes—
455C3×C4⋊C4C22×D312yes—
456C3×C4⋊C4C22×D312yes—
457C3×C22⋊C4—34no—
458C3×C22⋊C4—34no—
459C3×C22⋊C4—32no—
460C3×C22⋊C4—34no—
461C3×C42—21no—
462C3×C42—31no—
463C3×C42—31no—
464C3×C42—31no—
465C3×C42—32no—
466C3×C42C22×D311yescharacteristic
467C3×C42C22×D311yescharacteristic
468#217—34no—
469#217—34no—
470#217—34no—
471#217—32no—
472#217—32no—
473#217—34no—
474#217—32no—
475#217—32no—
476(C2×D3)⋊C4—32no—
477(C2×D3)⋊C4—32no—
478(C2×D3)⋊C4—34no—
479(C2×D3)⋊C4—32no—
480(C2×D3)⋊C4—34no—
481(C2×D3)⋊C4—34no—
482(C2×D3)⋊C4—32no—
483(C2×D3)⋊C4—34no—
484(C2×D3)⋊C4C22×D312yes—
485(C2×D3)⋊C4C22×D314yes—
486(C2×D3)⋊C4C22×D314yes—
487(C2×D3)⋊C4C22×D314yes—
488C4⋊Dic3—31no—
489C4⋊Dic3—31no—
490C4⋊Dic3—31no—
491C4⋊Dic3—31no—
492C4⋊Dic3—32no—
493C4⋊Dic3—32no—
494C4⋊Dic3—32no—
495C4⋊Dic3—32no—
496C4⋊Dic3—61no—
497C4⋊Dic3—61no—
498C4⋊Dic3C22×D311yescharacteristic
499C4⋊Dic3C22×D311yescharacteristic
500C4⋊Dic3C22×D314yes—
501Dic3⋊C4—32no—
502Dic3⋊C4—32no—
503Dic3⋊C4—32no—
504Dic3⋊C4—32no—
505Dic3⋊C4—34no—
506Dic3⋊C4—34no—
507Dic3⋊C4—34no—
508Dic3⋊C4—34no—
509Dic3⋊C4—32no—
510Dic3⋊C4—32no—
511Dic3⋊C4—32no—
512Dic3⋊C4—32no—
513Dic3⋊C4—32no—
514Dic3⋊C4—32no—
515Dic3⋊C4—32no—
516Dic3⋊C4—32no—
517Dic3⋊C4—62no—
518Dic3⋊C4—62no—
519Dic3⋊C4—64no—
520Dic3⋊C4—64no—
521Dic3⋊C4C22×D312yes—
522Dic3⋊C4C22×D314yes—
523C4×Dic3—32no—
524C4×Dic3—32no—
525C4×Dic3—32no—
526C4×Dic3—32no—
527C4×Dic3—34no—
528C4×Dic3—34no—
529C4×Dic3—32no—
530C4×Dic3—32no—
531C4×Dic3—32no—
532C4×Dic3—32no—
533C4×Dic3—62no—
534C4×Dic3—62no—
535C4×Dic3—64no—
536C4×Dic3C22×D311yescharacteristic
537C4×Dic3C22×D312yes—
538C4×Dic3C22×D311yescharacteristic
539C4×Dic3C22×D311yescharacteristic
540C22×C32C2511yescharacteristic
541C2×C3×D3—21no—
542C2×C3×D3—21no—
543C2×C3×D3—24no—
544C2×C3×D3—22no—
545C2×C3×D3—24no—
546C2×C3×D3—22no—
547C2×C3×D3—22no—
548C2×C3×D3—24no—
549C2×C3×D3H(5,𝔽2)12yes—
550C32×C4—21no—
551C32×C4—24no—
552C32×C4C2×#4112yes—
553C32×C42−1+412yes—
554C3⋊Dic3—22no—
555C3⋊Dic3—22no—
556C3⋊Dic3—22no—
557C3⋊Dic3C2×#4114yes—
558C3×Dic3—22no—
559C3×Dic3—22no—
560C3×Dic3—21no—
561C3×Dic3—22no—
562C3×Dic3—21no—
563C3×Dic3—21no—
564C2×#41—32no—
565C2×#41—92no—
566C2×#41—94no—
567C22×Q8—91no—
568C4⋊Q8—94no—
569C4⋊Q8—92no—
570C4⋊Q8—92no—
571C4⋊Q8D3211yescharacteristic
572#127—31no—
573#127—92no—
574#126—92no—
575#126—94no—
576#125—32no—
577#125—91no—
578#124—32no—
579#124—91no—
580#124—92no—
581#124—94no—
582#124—94no—
583#124—92no—
584#123—92no—
585#123—94no—
586#123—94no—
587#123—94no—
588#123—94no—
589C22⋊Q8—34no—
590C22⋊Q8—32no—
591C22⋊Q8—94no—
592C22⋊Q8—94no—
593C22⋊Q8—91no—
594C22⋊Q8—94no—
595#121—32no—
596#121—32no—
597#121—94no—
598#121—94no—
599#121—91no—
600#121—92no—
601C4×Q8—31no—
602C4×Q8—92no—
603C4×Q8—91no—
604C4×Q8—92no—
605C4×Q8—91no—
606C4×Q8—92no—
607C4×Q8—92no—
608C4×Q8—91no—
609C4×Q8—91no—
610C4×D4—32no—
611C4×D4—32no—
612C4×D4—32no—
613C4×D4—31no—
614C4×D4—92no—
615C4×D4—94no—
616C4×D4—92no—
617C4×D4—94no—
618C4×D4—92no—
619C4×D4—94no—
620C4×D4—92no—
621#117—92no—
622#117—94no—
623C2×C4⋊C4—32no—
624C2×C4⋊C4—92no—
625C2×C4⋊C4—91no—
626C2×C4⋊C4—94no—
627C2×C42—31no—
628C2×C42—92no—
629C23×C3—31no—
630C23×C3—34no—
631C23×C3—32no—
632C22×D3C23×D314yes—
633C22×D3C23×D312yes—
634C22×D3C23×D311yescharacteristic
635C3×Q8—42no—
636C3×Q8—42no—
637C3×Q8—62no—
638C3×Q8—82no—
639C3×D4—68no—
640C3×D4—64no—
641C3×D4—64no—
642C3×D4—62no—
643C3×D4—122no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—24no—
647C2×C3×C4—21no—
648C2×C3×C4—31no—
649C2×C3×C4—32no—
650C2×C3×C4—32no—
651C2×C3×C4—31no—
652C2×C3×C4—31no—
653C2×C3×C4—32no—
654C2×C3×C4—62no—
655C2×C3×C4—62no—
656C2×C3×C4—62no—
657C2×C3×C4—64no—
658C2×C3×C4—124no—
659C2×C3×C4—124no—
660C2×C3×C4C23×D314yes—
661C2×C3×C4C23×D314yes—
662C2×C3×C4C23×D311yescharacteristic
663C2×C3×C4C23×D311yescharacteristic
664C2×C3×C4C23×D311yescharacteristic
665C2×C3×C4C23×D311yescharacteristic
666C2×C3×C4C23×D311yescharacteristic
667C2×C3×C4C23×D311yescharacteristic
668#67—68no—
669#67—68no—
670#67—64no—
671#67—64no—
672#67—124no—
673#67—124no—
674C2×Dic3—32no—
675C2×Dic3—32no—
676C2×Dic3—32no—
677C2×Dic3—32no—
678C2×Dic3—32no—
679C2×Dic3—32no—
680C2×Dic3—32no—
681C2×Dic3—32no—
682C2×Dic3—62no—
683C2×Dic3—62no—
684C2×Dic3—62no—
685C2×Dic3—62no—
686C2×Dic3—64no—
687C2×Dic3—68no—
688C2×Dic3—64no—
689C2×Dic3—124no—
690C2×Dic3C23×D311yescharacteristic
691C2×Dic3C23×D312yes—
692C2×Dic3C23×D312yes—
693C2×Dic3C23×D311yescharacteristic
694C2×Dic3C23×D311yescharacteristic
695C2×Dic3C23×D312yes—
696D12—28no—
697D12—22no—
698D12—24no—
699D12—24no—
700D12—42no—
701C4×D3—22no—
702C4×D3—24no—
703C4×D3—22no—
704C4×D3—22no—
705C4×D3—44no—
706C4×D3—44no—
707C4×D3—68no—
708C4×D3—64no—
709C4×D3—64no—
710C4×D3—124no—
711Dic6—22no—
712Dic6—34no—
713Dic6—34no—
714Dic6—64no—
715Dic6—64no—
716Dic6—64no—
717Dic6—64no—
718Dic6—62no—
719Dic6—62no—
720Dic6—124no—
721Dic6—124no—
722Dic6—244no—
723C2×C32C22×#4111yescharacteristic
724C2×C32C2×H(5,𝔽2)11yescharacteristic
725C2×C32C2×2−1+411yescharacteristic
726C3×D3—22no—
727C3×D3—42no—
728C3×D3—44no—
729#41—124no—
730#41—188no—
731#41—368no—
732C2×Q8—31no—
733C2×Q8—92no—
734C2×Q8—91no—
735C2×Q8—91no—
736C2×Q8—94no—
737C2×Q8—184no—
738C2×Q8C2×D3212yes—
739C2×D4—31no—
740C2×D4—32no—
741C2×D4—32no—
742C2×D4—34no—
743C2×D4—32no—
744C2×D4—94no—
745C2×D4—92no—
746C2×D4—94no—
747C22×C4—31no—
748C22×C4—31no—
749C22×C4—31no—
750C22×C4—32no—
751C22×C4—34no—
752C22×C4—34no—
753C22×C4—92no—
754C22×C4—92no—
755C22×C4—94no—
756C22×C4—94no—
757C4⋊C4—31no—
758C4⋊C4—34no—
759C4⋊C4—32no—
760C4⋊C4—31no—
761C4⋊C4—34no—
762C4⋊C4—92no—
763C4⋊C4—92no—
764C4⋊C4—92no—
765C4⋊C4—92no—
766C4⋊C4—92no—
767C4⋊C4—92no—
768C4⋊C4—94no—
769C4⋊C4—92no—
770C4⋊C4—91no—
771C4⋊C4—91no—
772C4⋊C4—94no—
773C4⋊C4—92no—
774C4⋊C4C2×D3212yes—
775C4⋊C4C2×D3212yes—
776C22⋊C4—34no—
777C22⋊C4—34no—
778C22⋊C4—32no—
779C22⋊C4—34no—
780C22⋊C4—92no—
781C22⋊C4—92no—
782C22⋊C4—94no—
783C22⋊C4—92no—
784C22⋊C4—94no—
785C22⋊C4—94no—
786C22⋊C4—92no—
787C22⋊C4—94no—
788C42—31no—
789C42—31no—
790C42—31no—
791C42—32no—
792C42—92no—
793C42—92no—
794C42—92no—
795C42—94no—
796C42—92no—
797C42C2×D3211yescharacteristic
798C22×C3—21no—
799C22×C3—32no—
800C22×C3—61no—
801C22×C3—61no—
802C22×C3—62no—
803C22×C3—64no—
804C22×C3—64no—
805C22×C3—62no—
806C22×C3—62no—
807C22×C3—64no—
808C22×C3C24×D311yescharacteristic
809C22×C3C24×D311yescharacteristic
810C2×D3—21no—
811C2×D3—21no—
812C2×D3—24no—
813C2×D3—22no—
814C2×D3—22no—
815C2×D3—24no—
816C2×D3—24no—
817C2×D3—22no—
818C2×D3#100412yes—
819C3×C4—24no—
820C3×C4—21no—
821C3×C4—24no—
822C3×C4—21no—
823C3×C4—22no—
824C3×C4—22no—
825C3×C4—44no—
826C3×C4—41no—
827C3×C4—62no—
828C3×C4—61no—
829C3×C4—61no—
830C3×C4—62no—
831C3×C4—62no—
832C3×C4—61no—
833C3×C4#100712yes—
834C3×C4D3×#4112yes—
835C3×C4D3×#4112yes—
836C3×C4#101012yes—
837Dic3—21no—
838Dic3—22no—
839Dic3—21no—
840Dic3—22no—
841Dic3—21no—
842Dic3—22no—
843Dic3—34no—
844Dic3—34no—
845Dic3—64no—
846Dic3—64no—
847Dic3—62no—
848Dic3—62no—
849Dic3—62no—
850Dic3—62no—
851Dic3—62no—
852Dic3—62no—
853Dic3—122no—
854Dic3—122no—
855C32#352211yescharacteristic, complemented, Sylow
856C23—31no—
857C23—32no—
858C23—34no—
859Q8—42no—
860Q8—62no—
861Q8—94no—
862Q8—184no—
863Q8—182no—
864Q8—364no—
865D4—68no—
866D4—62no—
867D4—64no—
868D4—64no—
869D4—122no—
870D4—188no—
871D4—184no—
872D4—364no—
873C2×C4—31no—
874C2×C4—31no—
875C2×C4—31no—
876C2×C4—32no—
877C2×C4—32no—
878C2×C4—32no—
879C2×C4—62no—
880C2×C4—62no—
881C2×C4—62no—
882C2×C4—64no—
883C2×C4—92no—
884C2×C4—92no—
885C2×C4—92no—
886C2×C4—92no—
887C2×C4—124no—
888C2×C4—124no—
889C2×C4—184no—
890C2×C4—188no—
891C2×C4—184no—
892C2×C4—364no—
893C2×C4C22×D3211yescharacteristic
894C2×C4C22×D3214yes—
895C2×C4C22×D3211yescharacteristic
896C2×C4C22×D3211yescharacteristic
897C2×C3—21no—
898C2×C3—21no—
899C2×C3—21no—
900C2×C3—62no—
901C2×C3—124no—
902C2×C3—122no—
903C2×C3C2×#100411yescharacteristic
904C2×C3C2×#100711yescharacteristic
905C2×C3C2×D3×#4111yescharacteristic
906C2×C3C2×D3×#4111yescharacteristic
907C2×C3C2×#101011yescharacteristic
908C2×C3D3×H(5,𝔽2)11yescharacteristic
909D3—22no—
910D3—42no—
911D3—44no—
912C22—32no—
913C22—61no—
914C22—61no—
915C22—62no—
916C22—64no—
917C22—62no—
918C22—64no—
919C22—62no—
920C22—64no—
921C22C23×D3211yescharacteristic
922C4—21no—
923C4—24no—
924C4—61no—
925C4—62no—
926C4—61no—
927C4—62no—
928C4—61no—
929C4—62no—
930C4—94no—
931C4—182no—
932C4—182no—
933C4—182no—
934C4#6431512yes—
935C4#6431912yes—
936C3—21no—
937C3#8622911yescharacteristic, complemented
938C3#8693611yescharacteristic, complemented
939C2—62no—
940C2—122no—
941C2—124no—
942C2D3×#100411yescharacteristic
943C2C2×#6431511yescharacteristic
944C2C2×#6431911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4⋊Q8C22
hypercenterC4⋊Q8D32
hypocenterC32#3522
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #10596193C2semidirect
2. C3×#5730C2semidirect
3. C3×#5725C2semidirect
4. #10595391C2semidirect
5. #10595357C2semidirect
6. #10594592C2semidirect
7. #10594582C2semidirect
8. #10594525C2semidirect
9. #10594485C2semidirect
10. #10594427C2semidirect
11. #10594370C2semidirect
12. #10594367C2semidirect
13. #10594359C2semidirect
14. #10593974C2semidirect
15. #10593951C2semidirect
16. #10593906C2semidirect
17. C4×D3×Dic6C2semidirect
88. #5730D3semidirect
89. #5725D3semidirect
342. #634#41semidirect
855. C32#3522semidirect
937. C3#86229semidirect
938. C3#86936semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#105961932
C3×#57302
C3×#57252
#105953912
#105953572
#105945922
#105945822
#105945252
#105944852
#105944272
#105943702
#105943672
#105943592
#105939742
#105939512
#105939062
C4×D3×Dic62
#869363
#862293